^{1}and David L. Andrews

^{1,a)}

### Abstract

In a molecular system of energy donors and acceptors, resonanceenergy transfer is the primary mechanism by means of which electronic energy is redistributed between molecules, following the excitation of a donor. Given a suitable geometric configuration it is possible to completely inhibit this energy transfer in such a way that it can only be activated by application of an off-resonant laser beam: this is the principle of optically controlled resonanceenergy transfer, the basis for an all-optical switch. This paper begins with an investigation of optically controlled energy transfer between a single donor and acceptor molecule, identifying the symmetry and structural constraints and analyzing in detail the dependence on molecular energy level positioning. Spatially correlated donor and acceptor arrays with linear, square, and hexagonally structured arrangements are then assessed as potential configurations for all-optical switching. Built on quantum electrodynamical principles the concept of transfer fidelity, a parameter quantifying the efficiency of energy transportation, is introduced and defined. Results are explored by employing numerical simulations and graphical analysis. Finally, a discussion focuses on the advantages of such energy transfer based processes over all-optical switching of other proposed forms.

We are grateful to the Leverhulme Trust for providing the financial support for this project.

I. INTRODUCTION

II. COUPLING PAIR

III. ONE-DIMENSIONAL LINEAR ARRAYS

IV. TWO-DIMENSIONAL SQUARE-LATTICE ARRAYS

V. TWO-DIMENSIONAL HEXAGONAL-LATTICE ARRAYS

VI. CONCLUSION

### Key Topics

- Energy transfer
- 31.0
- Optical switching
- 13.0
- Irradiance
- 8.0
- Electric dipole moments
- 7.0
- Tensor methods
- 4.0

## Figures

Artistic impression of parallel two-dimensional donor and acceptor arrays, each arranged in the form of a hexagonal lattice.

Artistic impression of parallel two-dimensional donor and acceptor arrays, each arranged in the form of a hexagonal lattice.

Four Feynman diagrams for OCRET. Here, ∣0⟩ represents a molecule in the ground state; and relate to the excited state of the donor (on the left) and acceptor (right), respectively, with and as the corresponding intermediate states. In detail, diagram (a) depicts an instantaneous mechanism involving photon absorption and emission at the donor and acceptor, respectively, with a coupling photon created at the donor and annihilated at the acceptor; thus excitation is transferred from to . Diagrams (b), (c), and (d) are permutations that will achieve an identical final result.

Four Feynman diagrams for OCRET. Here, ∣0⟩ represents a molecule in the ground state; and relate to the excited state of the donor (on the left) and acceptor (right), respectively, with and as the corresponding intermediate states. In detail, diagram (a) depicts an instantaneous mechanism involving photon absorption and emission at the donor and acceptor, respectively, with a coupling photon created at the donor and annihilated at the acceptor; thus excitation is transferred from to . Diagrams (b), (c), and (d) are permutations that will achieve an identical final result.

Energy scheme for OCRET from to . Here, vertical arrows denote four interactions coupling the donor decay to the acceptor excitation . The directly involved energy levels are: , representing the ground electronic state for each molecule, and; and , the electronic excited states of and , respectively. Each state has its own vibrational manifold. Dashed lines denote virtual states, the closest energy levels and (not directly involved in the process, depicted in gray) being offset in energy by and . The horizontal arrow signifies energy transfer.

Energy scheme for OCRET from to . Here, vertical arrows denote four interactions coupling the donor decay to the acceptor excitation . The directly involved energy levels are: , representing the ground electronic state for each molecule, and; and , the electronic excited states of and , respectively. Each state has its own vibrational manifold. Dashed lines denote virtual states, the closest energy levels and (not directly involved in the process, depicted in gray) being offset in energy by and . The horizontal arrow signifies energy transfer.

Energy level positionings of states ∣0⟩, , and for donor and their corresponding symmetry classes for point group symmetry . Both possible classes of intermediate state, i.e., or , are shown, and the transformation properties for each allowed transition are indicated.

Energy level positionings of states ∣0⟩, , and for donor and their corresponding symmetry classes for point group symmetry . Both possible classes of intermediate state, i.e., or , are shown, and the transformation properties for each allowed transition are indicated.

As Fig. 4 caption, but for point group symmetry .

As Fig. 4 caption, but for point group symmetry .

Orientations of the relevant transition dipole moments for both donor and acceptor , determined for each of the possible intermediate state symmetries. These are illustrated for the point groups: (a) and (b) .

Orientations of the relevant transition dipole moments for both donor and acceptor , determined for each of the possible intermediate state symmetries. These are illustrated for the point groups: (a) and (b) .

Graphical depiction of parallel one-dimensional linear-lattice arrays. Here, represents the lattice constant and the displacement of the upper donor array from the lower acceptor array. The optically active molecules, each labeled with an integer coordinate, are denoted by pale ellipses (ground state) or a dark ellipse (excited state).

Graphical depiction of parallel one-dimensional linear-lattice arrays. Here, represents the lattice constant and the displacement of the upper donor array from the lower acceptor array. The optically active molecules, each labeled with an integer coordinate, are denoted by pale ellipses (ground state) or a dark ellipse (excited state).

Plot of , where is the time-dependent probability, against the aspect ratio for optical transfer from an excited molecule in the donor linear array to the required destination in the acceptor linear array (0-0); also depicted are the “cross-talk” probabilities for transfer to another molecule in either the acceptor or the donor array, and the sum of all three transfer possibilities (total). (Inset) difference between logarithms of the 0-0 and the sum probabilities for various , signifying on a logarithmic scale the *transfer fidelity*; on the ordinate axis each increment corresponds to 2.3% loss.

Plot of , where is the time-dependent probability, against the aspect ratio for optical transfer from an excited molecule in the donor linear array to the required destination in the acceptor linear array (0-0); also depicted are the “cross-talk” probabilities for transfer to another molecule in either the acceptor or the donor array, and the sum of all three transfer possibilities (total). (Inset) difference between logarithms of the 0-0 and the sum probabilities for various , signifying on a logarithmic scale the *transfer fidelity*; on the ordinate axis each increment corresponds to 2.3% loss.

Structure of the two-dimensional square-lattice arrays, viewed from above. Both lie in the plane, with all donor transition moments (black) in the upper array parallel to the axis, and all acceptor transition moments (gray) in the lower array parallel to the axis. The open arrows represent one excited donor and its counterpart acceptor. By reducing both arrays to a single row or column an equivalent graphical representation to Fig. 7 is found.

Structure of the two-dimensional square-lattice arrays, viewed from above. Both lie in the plane, with all donor transition moments (black) in the upper array parallel to the axis, and all acceptor transition moments (gray) in the lower array parallel to the axis. The open arrows represent one excited donor and its counterpart acceptor. By reducing both arrays to a single row or column an equivalent graphical representation to Fig. 7 is found.

Graph illustrating against for pair of two dimensional square arrays. Here, the irradiance of the input laser is and the key is that of Fig. 8.

Graph illustrating against for pair of two dimensional square arrays. Here, the irradiance of the input laser is and the key is that of Fig. 8.

Graph as Fig. 10, but for .

Graph as Fig. 10, but for .

In-plane coordinate system for a two-dimensional hexagonal lattice.

In-plane coordinate system for a two-dimensional hexagonal lattice.

Graph illustrating against for pair of two dimensional hexagonal arrays. Here, the irradiance of the input laser is .

Graph illustrating against for pair of two dimensional hexagonal arrays. Here, the irradiance of the input laser is .

Graph as Fig. 13, but for .

Graph as Fig. 13, but for .

## Tables

List of the relevant transition dipole moments and their orientations for the donor and acceptor.

List of the relevant transition dipole moments and their orientations for the donor and acceptor.

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